S.R. Venkatesh

Identification in the presence of classes of unmodeled dynamics and noise

Identification involves obtaining a model from an a priori chosen model class(es) using finite corrupted data. The corruption may be due to several reasons ranging from noise to unmodeled dynamics, since the real system may not belong to the model class. Two popular approaches-probabilistic and set-membership identification-deal with this problem by imposing temporal constraints on the noise sample paths. We differentiate between the two sources of error by imposing different types of constraints on the corruption. If the source of corruption is noise, we model it by imposing temporal constraints on the possible realizations of noise. On the other hand, if it results from unmodeled dynamics informational constraints are imposed. Contrary to probabilistic identification where the parameters of the identified model converge to the true parameters in the presence of noise, current results in set-membership identification do not have this convergence property. Our approach leads to bridging this gap between probabilistic and set-membership identification when the source of corruption is noise. For the case when both unmodeled dynamics and noise are present, we derive consistency results for the case when the unmodeled dynamics can be described either by a linear time-invariant system or by a static nonlinearity.

On system identification of complex systems from finite data

We introduce a new principle for identification based on choosing a model from the model-parameterization, which best approximates the unknown real system belonging to a more complex space of systems that do not lend themselves to a finite-parameterization. The principle is particularly effective for robust control as it leads to a precise notion of parametric and nonparametric error, and the identification problem can be equivalently perceived as that of robust convergence of the parameters in the face of unmodeled errors. The main difficulty in its application stems from the interplay of noise and unmodeled dynamics and requires developing novel two-step algorithms that amount to annihilation of the unmodeled error followed by averaging out the noise. The paper establishes: robust convergence for a large class of systems, topologies, and unmodeled errors; sample path based finite-time polynomial rate of convergence; and annihilation-correlation algorithms for linearly parameterized model structures.

Robust control of vertical motions in ultra-high rise elevators☆

Abstract The advent of ultra-high rise buildings has brought control over elevator vertical motion to the forefront. Unlike traditional low/mid-rise elevators, relatively high speed coupled with long rope lengths result in the need to address flexible low-frequency modes and non-linear dynamics. Research in this direction has only been initiated recently and primarily confined to the industry. This paper presents a practical methodology for designing high-performance controllers for elevator vertical motion for high-rise buildings. The methodology is directed towards satisfying several needs including scalability and ease of tuning of the control system. The former is important for adaptability to different hoistways, while the latter becomes necessary on account of performance degradation, experienced due to normal wear and tear. This is accomplished by developing a scalable lumped parameter model at several ultra-high rise hoistways leading to an alternate scalable empirical model based on a few prominent features in the vertical dynamics. A tunable controller based only on these features is developed. Simulation studies show that the controller meets a set of standardized tests that are typically used for evaluating elevator performance. A problem that arises in an ultra-high rise on account of the changing nature of dynamics as the elevator transits from one floor to another leading to the question of closed-loop non-linear stability is not a feature of the standardized tests. The problem of stability around a trajectory is reduced to a multi-variable Popov criterion and the tunable controller is shown to meet these requirements

Classical system identification in a deterministic setting

To reconcile identification with robust control, researchers have focused their attention on worst case identification. However, with assumptions such as unknown but bounded noise, worst case identification, leads to conservative bounds. Furthermore, these bounds are obtained at exponential cost. On the other hand in traditional identification, one obtains confidence bounds at polynomial cost. To overcome these shortcomings we explore several relaxations and restrictions on the worst case identification problem. In particular, we develop deterministic equivalent of stochastic identification.

Examples of extreme cases in i 1 and H ∞ optimization

Abstract We are guided by the simple bound ∥h∥ l1 ⩽ (2N + 1) ∥ h ∥ H ∞ established in [1], for finite dimensional systems, where ∥ h ∥l1 is the peak gain of the system and ∥ ^h ∥ H ∞ is the maximum frequency response of the system and N is the McMillan degree, to establish bounds on closed-loop systems resulting from l1 and H ∞ minimization. Furthermore, we illustrate that the effectiveness of adding frequency constraints in addition to the interpolation constraints in the l 1 minimization problem depends on the bandwidth of the plant.

Controller design and implementation for large-scale systems, a block decoupling approach

In this paper, implementation and controller design issues are considered for a class of large-scale systems. The idea of block decoupling is used as the main tool to achieve great simplification and complexity reduction. Linear input flow constraints are also considered. Two application examples illustrate the main ideas on the paper.

Examples of extreme cases in l 1 and H ∞ optimization

Advances in the theory of robust control have brought forth two methodologies for controller design: l/sub 1/ and H/sub /spl infin//. In this paper the authors take the approach of using examples to illustrate some tradeoffs while designing controllers using either of the two methodologies. Further, for the sake of simplicity the authors consider the case of minimization of the sensitivity transfer function in all the examples. First, the authors discuss the frequency domain properties of l/sub 1/ optimal solutions and compare them with H/sub /spl infin// optimal solutions. Next the authors contrast l/sub 1/ and H/sub /spl infin// optimal solutions and explore their extreme behavior. Finally with the help of an example the authors illustrate some interesting properties of mixed minimization.<<ETX>>

Block decoupling of linear systems

The Kronecker product of matrices is used to achieve the decomposition of finite dimensional linear systems into a set of decoupled systems of smaller dimension. A class of systems is specified for which such decomposition can be carried out. Two particular cases of application are studied.

Identification in the presence of bounded low-correlated noise

In this paper, we consider the problem of identification of discrete-time, single-input single-output linear time-invariant systems. The prior information about the unknown plant is that it belongs to a certain set of LTI systems. The plant can be identified using input-output experiments, where the input can be chosen freely and the observed output is corrupted by an additive disturbance which is assumed to be bounded and has low-correlation. This set of disturbance includes uniformly bounded sequences that satisfy a time averages correlation condition. The motivation for using such a disturbance set is that the disturbances resemble stochastic white noise processes. In particular, a white noise signal belongs to this set with high probability if the bound on the correlations approaches zero at a certain rate. This paper analyzes the problem of worst-case identification in the presence of the above set of disturbances.

Examples of extreme cases in l/sub 1/ and H/sub /spl infin// optimization

Advances in the theory of robust control have brought forth two methodologies for controller design: l/sub 1/ and H/sub /spl infin//. In this paper the authors take the approach of using examples to illustrate some tradeoffs while designing controllers using either of the two methodologies. Further, for the sake of simplicity the authors consider the case of minimization of the sensitivity transfer function in all the examples. First, the authors discuss the frequency domain properties of l/sub 1/ optimal solutions and compare them with H/sub /spl infin// optimal solutions. Next the authors contrast l/sub 1/ and H/sub /spl infin// optimal solutions and explore their extreme behavior. Finally with the help of an example the authors illustrate some interesting properties of mixed minimization.<<ETX>>